Chelsea's Benayoun came on to rapturous applause from the capacity home crowd of 14,000 at Tel Aviv's compact Bloomfield Stadium in the 71st minute. It was his first action for club or country since injuring an Achilles in September.
Ben Chaim scored in the 59th minute, seven minutes after coming on to replace midfielder Bebars Natcho.
Left unmarked on the right side of the area he blasted home a pass from Elyaniv Barda after Maor Buzaglo had run down the left wing.
Israel dominated possession but rarely troubled Georgian goalkeeper Nukri Revishvili.
The result kept Israel very much in the hunt in a tight Group F, which Greece lead on 11 points. Croatia and Israel, who also beat Latvia 2-1 on Saturday, both have 10 with Georgia on nine.
Despite Israel's slender lead, the team's French coach Luis Fernandez said he felt confident to let Benayoun have a few minutes' action despite not having played for Chelsea since returning from injury.
"Yossi returned to training with Chelsea last month and he trained well with us and I said that in the two matches he will play a few minutes and I am happy... this win will do a lot for Yossi's confidence and for the rest of the team, we will need him in our upcoming fixtures," Fernandez told reporters.
Georgia coach Temur Ketsbaia said his side had paid a heavy price for an error.
"It wasn't a bad game, in the second half both teams played more attacking soccer but we made one mistake and paid the price for it... we had a very tough game gainst Croatia and it was too much for us today to continue to play at the same level," he said.
